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I need to write an algorithm that can find the roots of any equation (of the form y=f(x).
It would have to do it by testing X values at certain points and homing in on the root by finding the sign change. What is the most efficient method of doing this?
Are you considering equations with complex roots too?
e.g.
(x^2) = -2
"Any" equation is quite broad.
Not complex ones no. Only Y=0 (for now)
OK, not ANY curve then :rolleyes: :thumb:
I'm not doing this by re-arranging equations or any cheating like that, just by calculating the Y at certain X values and interpolating to find roots.
Function Get_Y_Value(x) 'can be treated as a "black box", we don't need to know the equation itself.
So you'll need some sort of heuristic method to produce a reasonable guess at a root, then decrease or increase x depending on whether you're too high or low.
You can scale the increase or decrease amount according to how far from y=0 you are, i.e. decrease the change as you approach y=0.
As for the initial guess, hmm..I don't know really. It probably doesn't matter if your guess is a long way off anyway as long as you use the change-scaling approach..
Also are you going to allow equations with no roots and detect that?
Its OK. I have sorted it out now. Cheers. :thumb: